I checked the $entity data through Dump::Data, and looks like an actual email. I did find that

my $bh   = $part->bodyhandle;
print "MIME Type: $type\n";
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will outputs all the parts.

But

my $bh   = $part->bodyhandle;
                print "MIME Type: $type\n";
                if (defined $bh) {
                    open(my $OUTFILE, ">", $bh->path) or die $!;
                    binmode($OUTFILE);
                    $bh->print(\$OUTFILE);
                    close($OUTFILE);
                } #End IF $bh defined
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the $bh-print, seems to 'overwrite' the attachments making them zero-length.

So I removed that part and my code works. I do need to look at MIME::Parser::Filer more to clean up my code.

I do appreciate everyone's input and this wonderful site.